Cones on a pointing out from a cylinder
Here's my attempt:
Use a particle hair system, using a vertex group for density, growing from the vertices of the sphere (or faces, adapt to taste).
Muck about with the scale of the end caps of the cylinder, and the number of segments of the sphere for you needs...
Anything like what you're after?

Can't work out how to throw the blend file on here so-

https://www.dropbox.com/s/z8hpfk6rpbjpvbs/SphereWithConicalHair.blend?dl=0

Cheers
Mark